The Gumbel (or Smallest Extreme Value (SEV) or the Smallest Extreme Value
Type I) distribution is one of a class of Generalized Extreme Value (GEV)
distributions used in modeling extreme value problems. The Gumbel is a
special case of the Extreme Value Type I distribution for maximums from
distributions with “exponential-like” tails, it may be derived by
considering a Gaussian process of measurements, and generating the pdf for
the maximum values from that set of measurements (see examples).

Parameters:

loc : float

The location of the mode of the distribution.

scale : float

The scale parameter of the distribution.

size : tuple of ints

Output shape. If the given shape is, e.g., (m,n,k), then
m*n*k samples are drawn.

The Gumbel (named for German mathematician Emil Julius Gumbel) was used
very early in the hydrology literature, for modeling the occurrence of
flood events. It is also used for modeling maximum wind speed and rainfall
rates. It is a “fat-tailed” distribution - the probability of an event in
the tail of the distribution is larger than if one used a Gaussian, hence
the surprisingly frequent occurrence of 100-year floods. Floods were
initially modeled as a Gaussian process, which underestimated the frequency
of extreme events.

It is one of a class of extreme value distributions, the Generalized
Extreme Value (GEV) distributions, which also includes the Weibull and
Frechet.